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NONLINEAR RANK-ONE MODIFICATION OF THE SYMMETRIC EIGENVALUE PROBLEM

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Journal of Computational Mathematics 2010年第2期28卷 218-234页

作者： Xin Huang zhaojun.bai Yangfeng Su School of Mathematical Sciences Fudan University Shanghai 200433 China Department of Computer Science and Department of Mathematics University of California Davis CA 95616 USA

Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteration and successive linear approximation method （SLAM）. The global convergence of the SLAM is proven under some mild assumptions. Numerical examples illustrate that the SLAM is the most robust method.

关键词： Nonlinear eigenvalue problem Rank-one modification Rank-one damping Low-rank damping Picard Successive linear approximation method Nonlinear Rayleigh quotient iteration Safeguard Global convergence.

Linear response eigenvalue problem solved by extended locally optimal preconditioned conjugate gradient methods

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Science China Mathematics 2016年第8期59卷 1443-1460页

作者： bai zhaojun LI RenCang LIN WenWei Department of Computer Science and Department of Mathematics University of California at DavisDavisCA 95616USA Department of Mathematics University of Texas at ArlingtonArlingtonTX 76019USA Department of Applied Mathematics Taiwan Chiao Tung UniversityHsinehu 300China

The locally optimal block preconditioned 4-d conjugate gradient method(LOBP4dC G) for the linear response eigenvalue problem was proposed by bai and Li(2013) and later was extended to the generalized linear response eigenvalue problem by bai and Li(2014). We put forward two improvements to the method: A shifting deflation technique and an idea of extending the search subspace. The deflation technique is able to deflate away converged eigenpairs from future computation, and the idea of extending the search subspace increases convergence rate per iterative step. The resulting algorithm is called the extended LOBP4 dC G(ELOBP4dC G).Numerical results of the ELOBP4 dC G strongly demonstrate the capability of deflation technique and effectiveness the search space extension for solving linear response eigenvalue problems arising from linear response analysis of two molecule systems.

关键词： eigenvalue problem linear response deflation conjugate-gradient deflation

CONVERGENCE ANALYSIS OF A LOCALLY ACCELERATED PRECONDITIONED STEEPEST DESCENT METHOD FOR HERMITIAN-DEFINITE GENERALIZED EIGENVALUE PROBLEMS

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Journal of Computational Mathematics 2018年第5期36卷 739-760页

作者： Yunfeng Cai zhaojun.bai John E. Pask N. Sukumar LMAM & School of Mathematical Sciences Peking University Beijing 100871 China Department of Computer Science and Department of Mathematics University of California Davis CA 95616 USA Physics Division Lawrence Livermore National Laboratory Livermore CA 94550 USA Department of Civil and Environmental Engineering University of California Davis CA 95616 USA

By extending the classical analysis techniques due to Samokish, Faddeev and Faddee- va, and Longsine and McCormick among others, we prove the convergence of the precon- ditioned steepest descent with implicit deflation （PSD-id） method for solving Hermitian- definite generalized eigenvalue problems. Furthermore, we derive a nonasymptotie estimate of the rate of convergence of the PSD-id method. We show that with a proper choice of the shift, the indefinite shift-and-invert preconditioner is a locally accelerated preconditioner, and is asymptotically optimal which leads to superlinear convergence Numerical examples are presented to verify the theoretical results on the convergence behavior of the PSD- id method for solving ill-conditioned Hermitian-definite generalized eigenvalue problems arising from electronic structure calculations. While rigorous and full-scale convergence proofs of preconditioned block steepest descent methods in practical use still largely eludes us, we believe the theoretical results presented in this paper shed light on an improved understanding of the convergence behavior of these block methods.

关键词： Eigenvalue problem Steepest descent method Preconditioning Superlinear convergence.

Contribution of Microbial Inter-kingdom Balance to Plant Health

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Molecular Plant 2019年第2期12卷 148-149页

作者： Chunlei Zhang Youming Zhang zhaojun Ding Yang bai StateKeyLaboratoryofMicrobialTechnology ShandongUniversityQingdaoShandong266237China StateKeyLaboratoryofPlantGenomics InstituteofGeneticsandDevelopmentalBiologyChineseAcademyofScienceBeijing100101China CAS-JICCentreofExcellenceforPlantandMicrobialScience InstituteofGeneticsandDevelopmentalBiologyChineseAcademyofSciencesBeijing100101China “UniversityofChineseAcademyofSciences CollegeofAdvaneedAgriculturalSciencesBeijing100039China TheKeyLaboratoryofPlantDevelopmentandEnvironmentalAdaptationBiology MinistryofEducationCollegeofLifeSciencesShandongUniversityQingdaoShandong266237China

Soil-borne fungal and oomycetal pathogens cause devastating agricultural losses every year. The abundance and diversity of filamentous eukaryotes in the roots of healthy plants are in flue need by root-associated bact... 详细信息

关键词： Microbial Inter-kingdom Balance Plant Health filamentous eukaryotes

A High-Quality Preconditioning Technique for Multi-Length-Scale Symmetric Positive Definite Linear Systems

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Numerical Mathematics(Theory,Methods and Applications) 2009年第4期2卷 469-484页

作者： Ichitaro Yamazaki zhaojun.bai Wenbin Chen Richard Scalettar Department of Computer Science University of California Davis CA 95616 USA School of Mathematical Sciences Fudan University Shanghai 200433 China Department of Physics University of California Davis CA95616 USA

We study preconditioning techniques used in conjunction with the conjugate gradient method for solving multi-length-scale symmetric positive definite linear systems originating from the quantum Monte Carlo simulation of electron interaction of correlated materials. Existing preconditioning techniques are not designed to be adaptive to varying numerical properties of the multi-length-scale systems. In this paper, we propose a hybrid incomplete Cholesky （HIC） preconditioner and demonstrate its adaptivity to the multi-length-scale systems. In addition, we propose an extension of the compressed sparse column with row access （CSCR） sparse matrix storage format to efficiently accommodate the data access pattem to compute the HIC preconditioner. We show that for moderately correlated materials, the HIC preconditioner achieves the optimal linear scaling of the simulation. The development of a linear-scaling preconditioner for strongly correlated materials remains an open topic.

关键词： Preconditioning multi-length-scale incomplete Cholesky factorization quantum MonteCarlo simulation.

Coal-bearing strata sequence stratigraphy of Paleogene Meihe Formation,Meihe Basin,NE China

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International Journal of Coal Science & Technology 2021年第4期8卷 547-561页

作者： Yueyue bai Qingtian Lii zhaojun Liu Pingchang Sun Rong Liu Shuqing Yao SinoProbe-China Deep Exploration Center Chinese Academy of Geological SciencesBeijng 100037China Key Laboratory for Oil Shale and Coexisting Minerals Mineralization and Exploration and Exploitation Jilin UniversityChangchun 130061China

The Meihe Basin is an important Paleogene coal-bearing basin located in the Dunhua-Mishan Fault Zone,northeastern *** on a comprehensive study of well logs,seismic profiles,cores and rock geochemical properties,the coal distribution,paleoenvironment evolution within a sequence stratigraphic framework and the accumulation model to explain how coal seams developed in small fault basin were discussed in ***-third-order sequences were identified in the Paleogene Meihe Formation of Meihe Basin and the two coal-bearing sequences are the Lower Coalbearing Member of Sequence I and the Upper Coal-bearing Member of Sequence *** three types of system tracts are developed in both sequences,i.e.,the lowstand systems tract(LST),the transgressive systems tract(TST),and the highstand systems tract(HST).In LST of Sequence I,fan delta plain marsh is the main coal accumulating environment where coal seams are thin,discontinuous and therefore uneconomic for mining,and it is the same with all coal seams developed in Sequence *** in TST and HST of Sequence I,lake swamp is the main sedimentary environment where coal seams are thick,continuous,widely distributed,and thus economically attractive for *** the study area,the nice thick economical coal seams are usually developed in an ideal stable depositional environment where organic matter accommodation space grows at a balanced rate with peat,in other words,free of sediment input or channel *** key findings of this study could provide guidance for the exploration of coal seams in the Meihe Basin and other similar basins.

关键词： Coal seam Sequence stratigraphy Fan delta Swamp Meihe Basin

Effect of Multi-Pass Equal Channel Angular Pressing on the Microstructure and Mechanical Properties of a Heterogeneous Mg_(88)Y_8Zn_4 Alloy

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Journal of Materials Science & Technology 2016年第12期32卷 1274-1281页

作者： Huan Liu zhaojun Cheng Kai Yan Jingli Yan Jing bai Jinghua Jiang Aibin Ma College of Mechanics and Materials Hohai University Ocean and Coastal Engineering Research Institute Hohai University College of Mechanical Engineering Yangzhou University Jiangsu Key Lab of Advanced Metallic Materials College of Materials Science and EngineeringSoutheast University

The microstructure evolutions and mechanical properties of a heterogeneous Mg88Y8Zn4（in at.%） alloy during multi-pass equal channel angular pressing（ECAP） were systematically investigated in this *** results show that four phases,i.e.α-Mg,18 R long period stacking ordered（LPSO） phase,Mg24Y5 and Y-rich phase,are present in cast *** ECAP,dynamic recrystallization（DRX） occurs and the diameter of DRXedα-Mg grains decreases to 0.8 μ***,precipitation of lamellar 14 H LPSO structure is developed withinα-Mg *** the refinement of α-Mg grains and precipitation of 14 H LPSO contribute to the increase in micro-hardness from 98 HV to 135 HV for α-*** addition,a simplified model describing the evolution of 18 R LPSO phase is established,which illustrates that 18 R undergoes a four-step morphological evolution with increasing strains during ECAP,*** lath → bent lath → cracked lath → smaller *** test results indicate that the alloy has been markedly strengthened after multi-pass ECAP,and the main reason for the significantly enhanced mechanical properties could be ascribed to the DRXed α-Mg grains,newly precipitated 14 H lamellas,18 R kinking and refined 18 R particles.

关键词： Magnesium alloys Equal channel angular pressing (ECAP) Long period stacking ordered (LPSO) phase Microstructure Mechanical property

AVP(4-8) Improves Cognitive Behaviors and Hippocampal Synaptic Plasticity in the APP/PS1 Mouse Model of Alzheimer’s Disease

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Neuroscience Bulletin 2020年第3期36卷 254-262页

作者： Xiumin Zhang Fang Zhao Chenfang Wang Jun Zhang Yu bai Fang Zhou zhaojun Wang Meina Wu Wei Yang Junhong Guo Jinshun Qi Department of Neurology First HospitalShanxi Medical UniversityTaiyuan 030001China Department of Physiology Key laboratory of Cellular PhysiologyMinistry of EducationShanxi Medical UniversityTaiyuan 030001China

Memory deficits with aging are related to the neurodegeneration in the brain, including a reduction in arginine vasopressin(AVP) in the brain of patients with Alzheimer’s disease(AD). AVP(4-8), different from its precursor AVP, plays memory enhancement roles in the CNS without peripheral side-effects. However, it is not clear whether AVP(4-8) can improve cognitive behaviors and synaptic plasticity in the APP/PS1 mouse model of AD. Here, we investigated for the first time the neuroprotective effects of AVP(4-8) on memory behaviors and in vivo long-term potentiation(LTP) in APP/PS1-AD *** results showed that:(1) APP/PS1-AD mice had lower spontaneous alternation in the Y-maze than wild-type(WT) mice, and this was significantly reversed by AVP(4-8);(2) the prolonged escape latency of APP/PS1-AD mice in the Morris water maze was significantly decreased by AVP(4-8), and the decreased swimming time in target quadrant recovered significantly after AVP(4-8) treatment;(3) in vivo hippocampal LTP induced by high-frequency stimulation had a significant deficit in the AD mice, and this was partly rescued by AVP(4-8);(4) AVP(4-8)significantly up-regulated the expression levels of postsynaptic density 95(PSD95) and nerve growth factor(NGF)in the hippocampus of AD mice. These results reveal the beneficial effects of AVP(4-8) in APP/PS1-AD mice,showing that the intranasal administration of AVP(4-8)effectively improved the working memory and long-term spatial memory of APP/PS1-AD mice, which may be associated with the elevation of PSD95 and NGF levels in the brain and the maintenance of hippocampal synaptic plasticity.

关键词： AVP(4-8) APP/PS1 transgenic mice Cognitive behavior Synaptic plasticity In vivo hippocampal LTP

Structural Basis of Glycan Recognition in Globally Predominant Human P[8]Rotavirus

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Virologica Sinica 2020年第2期35卷 156-170页

作者： Xiaoman Sun Lei Dang Dandi Li Jianxun Qi Mengxuan Wang Wengang Chai Qing Zhang Hong Wang Ruixia bai Ming Tan zhaojun Duan National Health Commission Key Laboratory for Medical Virology and Viral Diseases Beijing 102206China National Institute for Viral Disease Control and Prevention China CDC.Beijing 102206China Inner Mongolia Medical University Huhehaote 010059China Institute of Microbiology Chinese Academy of SciencesBeijing 100101China Glycosciences Laboratory Department of MedicineImperial College LondonLondonUK Division of Infectious Diseases University of Cincinnati College of MedicineCincinnatiOHUSA

Rotavirus(RV)causes acute gastroenteritis in infants and children *** studies showed that glycans such as histo-blood group antigens(HBGAs)function as cell attachment factors affecting RV host susceptibility and prevalence.P[8]is the predominant RV genotype in humans,but the structural basis of how P[8]RVs interact with glycan ligands remains *** this study,we characterized the interactions between P[8]VP8~*s and glycans which showed that VP8~*,the RV glycan binding domain,recognized both mucin core 2 and H type 1 antigens according to the ELISA-based oligosaccharide binding ***,we determined the structural basis of P[8]RV-glycans interaction from the crystal structures of a Rotateq P[8]VP8~*in complex with core 2 and H type 1 glycans at 1.82.3?,respectively,revealing a common binding pocket and similar binding *** and sequence analysis demonstrated that the glycan binding site is conserved among RVs in the P[Ⅱ]genogroup,while genotype-specific amino acid variations determined different glycan binding *** data elucidated the detailed structural basis of the interactions between human P[8]RVs and different host glycan factors,shedding light on RV infection,epidemiology,and development of anti-viral agents.

关键词： Rotavirus(RV)·P Glycan binding specificity VPS*structure Mucin core 2 Lacto-N-fucopentaose 1(LNFPl)